Séminaire
Because direct observations of the ocean's interior are sparse, satellite altimetry plays a crucial role in determining its time-dependent, three-dimensional velocity structure. Current methods of reconstructing flow at depth from surface observations assume that the three-dimensional flow can be represented as a sum of a small number of modes, or basis functions. At scales of order the deformation scale and larger, there is some observational evidence that surface motions are well-represented by the barotropic and first baroclinic interior modes. However, recent theoretical developments, supported by simulation and improved analysis of satellite altimetry, suggest that below the deformation scale, surface signals are not well-correlated with low-mode vertical structure.
Two recent reconstruction methods (which I will review) are based on the realization that standard interior modes cannot represent lateral surface buoyancy gradients, which drive a cascade of eddy buoyancy variance to small scales. These methods, which have been quite successful, append the low vertical modes by a wavenumber-dependent zero-PV mode that captures surface buoyancy dynamics. However, these modes are not orthogonal to each other, and so cannot provide a complete basis to represent the energy of the flow.
I will introduce a new modal decomposition that results from the simultaneous diagonalization of the energy and a generalization of potential enstrophy that includes contributions from the surface buoyancy field. This approach yields a family of orthonormal bases that depend on a free parameter: the standard baroclinic modes are recovered in a limiting case, while other choices provide modes that represent surface and interior dynamics in an efficient way.